The average number of miles [in thousands] that a car's tire will function before needing replacement is as and the standard deviation is It}. Suppose that 47:" randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? I ~ N[|:|,l:|} b. What is the distribution of :E? 5: ~ Ni:],:l} c. If a randomly selected individual tire is tested, find the probability that the number of miles [in thousands) before it will need replacement is between I54 and $3.3. |:| d. For the 4? tires tested, find the probability that the average miles [in thousands) before need of replacement is between I54 and 63.3. |:| e. For part d}, is the assumption that the distribution is normal necessary? CI NoCl1 'fes